COMET • Vol. 1, No. 37 – 18 December 2000


(1) New Curriculum Commissioner Named

The State Board of Education appointed Edith Crawford to the Curriculum Frameworks and Supplemental Materials Commission (a.k.a., Curriculum Commission) on December 6. (This is the Commission that recently voted on mathematics textbooks submissions.) She will serve a 4-year term to commence on January 1, 2001.

Crawford has a teaching background in English, History/Social Science and English Language Development . She currently works in the San Juan Unified School District (Sacramento) as vice principal at Mira Loma High School.

(2) “Governor Names Former Lawmaker as Top Education Adviser” by Jennifer Kerr -11 December 2000


A former Marin County lawmaker who authored school legislation for Gov. Gray Davis is his new top education adviser. The Democratic governor announced Monday that Kerry Mazzoni, 51, will be his second education secretary.

Davis has had two interim education secretary’s since former state Sen. Gary Hart resigned last winter after one year on the job.

Mazzoni, who formerly chaired the Assembly Education Committee, was long expected to get the job, but she could not be appointed until after her term expired on Nov. 30. She left office because of term limits.

“Kerry Mazzoni was a driving force for education during her tenure in the Legislature and now she brings invaluable experience to further my administration’s efforts to improve California schools,” Davis said in a statement.

The education secretary advises the governor on school-related matters and lobbies the Legislature for his proposals. The job is separate from the state Department of Education, which is headed by the elected superintendent, Delaine Eastin, and from the policy-setting state Board of Education, also appointed by the governor.

Mazzoni replaces John Mockler, a veteran education expert named interim secretary last summer. Before that, Susan Burr, who was undersecretary for Hart, was the interim before taking a job with the Elk Grove school district.

Mazzoni represented the 6th Assembly District from 1994 to 2000. She served on the Novato Unified School District board from 1987 to 1994 and was board president in 1990 and 1993.

During her time in the Assembly, Mazzoni worked on class-size reduction, teacher training, kindergarten readiness and school bond legislation. She was the author of Davis’ 1999 bill to create summer reading instruction academies and coauthor of his 2000 bill to expand advanced-placement courses in high schools.

She has a bachelor’s degree in child development from University of California, Davis. Her salary will be $118,524. The job does not require confirmation by the state Senate.

(3) Sacramento Bee Series on Algebra

Last week, COMET presented the first of a series of articles by Deb Kollars on algebra. Below are the remaining links for the articles in this series:

“Applied Math: Think Algebra’s Useless in Life? Think Again” (12 Dec 2000)

Have you crossed a bridge lately? Picked up a cell phone? Paid an insurance premium? Walked into a building? Earned or paid some compound interest? Been in a hospital? Signed on to a computer? If the answer is yes to any of these, you have encountered algebra — in all its glorious usefulness…

But the world is quite full of algebra. It helps make things happen. It matters…

Those without algebra have fewer career options. They may earn less money. And they miss out on one of the niftier things a thorough education has to offer: stretching a mind in ways that can end up serving a body well… Algebra is the basic language used in science, mathematics and computers. From there, its reach branches into a plethora of professions — engineering, architecture, medicine, marketing, finance, economics and agriculture, just to name a few… Even occupations that don’t seem very mathematical, such as psychology or sociology, require an understanding of algebra because these days so much of the work involves quantifying information.

“You are surrounded by algebra for heaven’s sake,” said Sherman K. Stein, a professor emeritus of mathematics at the University of California, Davis. “Every time you pick up your cell phone, you are identified as an algebraic formula,” he said. “You turn on the radio, if you looked at how the antennas are designed, you would find algebra. If you’re buying insurance, all those calculations about the life span of people who smoke and so forth, all of it involves algebra”…

In his 1996 book, “Strength in Numbers,” Stein went to considerable length to document the mathematical skill levels required in several hundred occupations. In the chapter called “What’s In It For Me?” Stein found that two-thirds of the American work force — about 80 million people out of 121 million — do not use algebra or math skills higher than basic arithmetic.

There is a price for dodging algebra and higher math. Many of those workers, Stein said, are clustered in jobs that pay far less — receptionists, stock clerks, janitors, waiters, guards, welders and truck drivers…

“Algebra: From Papyrus To PCs” (13 Dec 2000)

…Asking about the origins of algebra brings to mind a new take on that old question about the tree falling in the forest. If no one is there to calculate the arc of the fall, the distance traveled and the tree’s new relationship to the ground, does the tree still possess a new angle at which to repose?

The answer is yes, if you ask professor Scott Farrand, who teaches the history of mathematics at California State University, Sacramento. And what it means is this: Before anybody came up with the name, the x’s and all of those formulas, algebra was present in our world, waiting to be discovered. All it took was civilization.

In ancient times, when people started getting together and forming kingdoms, they had to figure out ways to keep track of the things they were doing: planting fields, building pyramids, selling sheep to one another and, in the case of the king, collecting taxes. Early on, most of that involved basic calculations, what we know today as simple arithmetic…

“After basic arithmetic, algebra and geometry were the next areas of math to come,” Farrand . “It was a gradual development. It would start with this, ‘There’s something I want to know,’ and take off from there”…

The earliest record we have of algebra is a scroll of papyrus dating to 1650 B.C. It was written by a scribe from Egypt named A’h-mose. Like many of Egypt’s treasures, it now rests in a museum in Britain.

Victor Katz, a professor of mathematics at the University of the District of Columbia and an algebra expert, saw the famous papyrus while traveling through London. The fragile scroll of reed-like material was ensconced in glass…

One of the interesting things about the papyrus is that many of its lessons did not reflect real-life questions, but rather focused on practicing problem-solving skills through repetitive questions. Translated, a typical question went something like this: “A quantity and its 1/7 added together become 19. What is the quantity?”

These practice questions were like the drills of modern-day textbooks. But this wasn’t learning for the masses. In those days in Egypt, only members of the priestly class were allowed access to such knowledge. You could call it the Algebra Attitude. In some ways, it still persists today. And even back then, it wasn’t just an Egyptian thing… As Katz [wrote] in a 1993 paper, the Babylonian lessons were designed “to learn various methods of reducing complicated problems to simpler ones – to train the minds of the future leaders of the country”…

But it wasn’t until about A.D. 825 that algebra got its name and its status as a textbook-worthy discipline. At that time, a scientist from Baghdad, named al-Khwarizmi wrote the first true text in algebra. He gave the text a long name that included the word “al-jabr.” The word referred to a mathematical operation in which a quantity subtracted from one side of an equation becomes an addition on the other side.

Since then, algebra has come to mean much more than this, but the word stuck and eventually became the name of the subject that would launch the rest of higher mathematics.

The al-Khwarizmi text marked a big moment for algebra. It was reproduced and eventually found its way to Europe , where it was translated into Latin. In about the 12th century, the Latin translation landed in the hands of Spanish, Italian and other European scholars, who began learning algebra for the first time. Those were heady days for Europe. Universities were popping up, and intellectual pursuits became fashionable.

“When al-Khwarizmi’s book fell into the hands of European scholars, it was very exciting for them,” Farrand said. The invention of the printing press in the mid-1400s spread the gospel of algebra even farther.

This is not to say, however, that the infusion of algebra rocked the planet.

“It was not like the steam engine or a silicon chip,” Farrand said. “Things didn’t dramatically change over any single generation. It was all very gradual.” As one example, up until the 12th century and beyond in some places, algebra consisted of prose on the page. It had none of the signature strings of letters, numbers and strange-looking notations that have caused generations of people to feel inadequate.

The shorthand and symbolism crept in slowly over the years. The first person whose algebra really began to look like ours today was Rene Descartes, the French philosopher who gave us that unforgettable line, “Cogito ergo sum” “I think, therefore I am.”

Descartes was a precise and orderly thinker, big on mathematics and objective, absolute truths. “In the search for the truth of things,” he wrote, “a method is indispensable.” It was he who first used letters from the tail end of the alphabet – x’s and y’s – to express unknown quantities. Why Descartes chose x and y as opposed to, say, f and g, remains a matter of great speculation among math…

Descartes died in 1650, and since then, what we now consider elementary algebra or Algebra 1 was pretty much in place.

An 18th century math whiz from Switzerland named Leonhard Euler put it all down in a thorough and respected book called “Complete Introduction to Algebra.” Today, a typical elementary or first-year algebra text is not much different from Euler’s text, although graphing was added toward the beginning of the early 20th century, Katz said.

During the last couple of hundred years, vast changes have taken place in the world of mathematics. Brilliant minds have developed more and more abstract layers of algebra that are taught at the university level.

The field of calculus took shape over a short period in the late 1600s as a way to answer deep questions about the nature of motion and curves. Computers continue to take the curious on to new mathematical frontiers.

But when it comes to math, nothing quite compares to basic algebra in terms of staying power and usefulness. “Out of all the math fields, algebra is the biggest,” Katz said. “Without it, you can’t do anything else.”

Farrand of CSUS agreed. He will tell you solemnly that he loves algebra as much as he likes to climb mountains and nearly as much as teaching. And here is why: “Algebra never fails”…

“State’s New Algebra Goals Are A Shock To The School System” (14 Dec 2000)

If American children went to school most anywhere else, their algebra experience would be vastly different… Here, many students never study it. Among those who do, most wait until their freshman year in high school or later. By then, it is an abrupt shift into the world of abstraction.

Not so in Germany, Japan, Argentina, Korea, France and other developed countries. In those nations, all students are expected to conquer beginning algebra. They start early — routinely in the sixth or seventh grade — and study it thoroughly until they reach high school.

“In the United States, only about 25 percent of students in the middle grades get algebra. Everywhere else, basically 100 percent get it at that point,” said William Schmidt, national coordinator of research for the Third International Mathematics and Science Study…

In the United States, students have tended to study basic arithmetic from kindergarten through eighth grade. Seventh and eighth grade are notorious for being wastelands of arithmetic — fractions, decimals, multiplication, division — that students have seen before.

Then boom, in ninth grade, students hit algebra — a mathematics course that is tough and abstract. They are expected to learn it in a single year. By the standards of other nations, Schmidt said, that is cruel and unusual punishment.

Most developed nations teach arithmetic through grade five or six. Then, for the next two or three years, students study beginning algebra at a pace that is slow and thorough. Most also learn geometry alongside algebra. By the time they reach high school, nearly all are ready for higher mathematics. Some may wind up going down a vocational or technical track rather than college prep, but that sorting process occurs after Algebra 1 and Geometry have been covered.

“In Asia, in Europe, it is so much more sensible and humane. The students have time to really absorb the material,” Schmidt said.

“Here, people are just plopped into algebra, and they end up struggling all year. It is only the brightest kids in mathematics who are able to make this abrupt shift. That’s why algebra is considered such an elite course.”

That stigma could be on its way out in California.

In the state’s new math standards, algebra turns up in kindergarten as a major theme. Although children may not hear the “A”-word for several years, the standards recommend that young minds be exposed from Day One to algebra’s earliest concepts…

No one expects eighth-grade algebra to happen everywhere, overnight. It will take years to get the books lined up, the standards in place and the teachers trained for the task…

“Lesson 2: The Simpler, the Better” (11 Dec 2000)

“Lesson 3: Another Way to Simplify” (12 Dec 2000)

“Lesson 4: Excellent Exponents” (13 Dec 2000)

“Final Exam” (14 Dec 2000)

“Helping with X” (tips for parents)



“Explaining Why Math Does Count” by Connie Langland

Source: Philadelphia Inquirer – 14 December 2000

Niiamah Ashong, a ninth grader, is on a fast track in math at Pennsauken High School. But he is not enrolled in algebra I, geometry or trigonometry, the traditional means of moving up the math ladder. Instead, he and his classmates are catching the latest wave in math instruction, a mix-and-match method that attempts to make, over and over, one point – that math matters.

Want to build a patio? Algebra rules! To decide whether a game of chance will be fair to all players, try geometry and probability! Will a singer sell more records if she goes on tour to promote her newest release? Look at the data, and figure out the statistics!

Math used to be “mostly just problems and numbers, sitting by yourself at a desk, not really thinking, just doing the math,” Niiamah said. “This way, we’re preparing for everything. And it’s more fun.”

Such words resound as music to the ears of math teachers. In the ongoing struggle to upgrade math education in this country, half the battle may be in convincing students that there are practical, long-term reasons to learn algebra, geometry, and more advanced mathematics.

Educators say too many students drop off the math track using traditional texts. They develop math phobia, teachers say. Math anxiety takes hold. Generations have opened a text to a page full of equations and asked: Who needs algebra, anyway?

The public, meanwhile, is digesting data, released just last week, that shows American eighth graders to be continuing to lag behind their peers in most industrialized countries in math and science achievement. These less-than-stellar scores from U.S. students were reported in an ongoing study, the Third International Mathematics and Science Study (TIMSS).

The TIMSS scores can be remedied if instruction is revamped, say educators like Lee Stiff, president of the National Council of Teachers of Mathematics (NCTM). Efforts to retool math instruction are broad based, in urban as well as suburban districts across the country, Stiff said.

And to the query “Who needs algebra,” Stiff answers that “algebraic reasoning” serves as the foundation for careers and fields of study as far-flung as sociology and the culinary arts. “The challenge,” Stiff said, “becomes one of mammoth proportions: to create courses that engage students, that students can understand and can get excited about”…

La Salle University’s Joseph Merlino… insists that children are natural-born mathematicians.

“Really, what algebra is about – what all of mathematics is about – [is] relations and patterns,” Merlino said. “That’s why little kids are really turned on to it.” But, he added, “that joy of a child learning math gets destroyed along the way because of the way math is taught. When you see patterns and relationships, that’s when you use it.”

Merlino is director of the Greater Philadelphia Secondary Mathematics Project at La Salle, which has a five-year National Science Foundation grant to teach math teachers new methods of instruction….

“I used to say, ‘When am I going to use this in real life?’ ” student Mike Soukup said. “Now, I know why.”

And Julian Johnson was exuberant expressing this thought: “If we were in a regular algebra class, we would be doing the exact same thing every day. In this class, we’re also doing geometry, calculus. . . . It’s just great. It’s wonderful.”



Presidential Awards for Excellence in Mathematics and Science Teaching

The Presidential Awards for Excellence in Mathematics and Science Teaching (PAEMST) Program was established in 1983 by The White House and is sponsored by the National Science Foundation (NSF). The program identifies outstanding science and mathematics teachers, kindergarten through 12th grade, in each state and the four U.S. jurisdictions.

Recognition is given to K-12 teachers in four award groups:(l) elementary mathematics, (2) elementary science, (3) secondary mathematics, and (4) secondary science. The secondary groups can include middle, junior, and senior high school teachers. Four Presidential Awards will be given in 2001 in each state and the four U.S. jurisdictions – up to a total of 216 awardees.

The Presidential Award includes:

= a $7,500 National Science Foundation grant to the awardee’s school, to be spent under the awardee’s direction over a five-year period, to improve school mathematics and science programs

= generous gifts to the awardees and their schools from private sector donors

= an expense-paid trip for the awardee and a guest to Washington, DC for a series of events which will include (a) an awards ceremony and presidential citation; (b) meetings with leaders in government and education; (c) workshops to share ideas and teaching experiences; and (d) honorary receptions and banquets.

For more information, visit the PAEMST Web site at

Application Deadline: February 12, 2001